In this tutorial, you will learn how radix sort works. Additionally, you will discover working instances of radix sort in C, C++, Java, and Python.

Radix sort, not at all like merge-sort or quick-sort, is a non-comparative sorting algorithm. The thought behind it is to sort a list of integers dependent on their individual digits. As such, sorting is performed from the least significant digit to the most significant digit.

Radix sort uses a similar thought behind count sort/bucker sort.

Radix sort is a sorting strategy that sorts the elements by first grouping the individual digits of similar place values. At that point, sort the elements as per their increasing/decreasing order.

Assume, we have an array of 8 elements. To start with, we will sort elements dependent on the value of the unit place. At that point, we will sort elements dependent on the value of the 10th place. This process goes on until the last huge spot.

Let the initial array be [121, 432, 564, 23, 1, 45, 788]. It is sorted by radixsort as demonstrated in the figure underneath.

If it’s not too much trouble, experience the counting sort before reading this article since counting sort is used as an intermediate sort in radix sort.

1. Locate the largest element in the array, for example, max. Let X be the number of digits in max. X is calculated on the grounds that we need to experience all the huge spots, of all elements.

In this array [121, 432, 564, 23, 1, 45, 788], we have the largest number 788. It has 3 digits. In this way, the loop should go up to hundreds places (3 times).

2. Presently, experience each critical spot individually.

Use any stable sorting procedure to sort the digits at each critical spot. We have used the counting sort for this.

Sort the elements dependent on the unit place digits (X=0).

3. Presently, sort the elements dependent on digits at tens place.

4. At last, sort the elements dependent on the digits at hundreds place.

```radixSort(array)
d <- maximum number of digits in the largest element
create d buckets of size 0-9
for i <- 0 to d
sort the elements according to ith place digits using countingSort

countingSort(array, d)
max <- find largest element among dth place elements
initialize count array with all zeros
for j <- 0 to size
find the total count of each unique digit in dth place of elements and
store the count at jth index in count array
for i <- 1 to max
find the cumulative sum and store it in count array itself
for j <- size down to 1
restore the elements to array
decrease count of each element restored by 1```

## Python, Java, and C/C++ Examples

Python

```# Radix sort in Python

# Using counting sort to sort the elements in the basis of significant places
def countingSort(array, place):
size = len(array)
output =  * size
count =  * 10

# Calculate count of elements
for i in range(0, size):
index = array[i] // place
count[index % 10] += 1

# Calculate cummulative count
for i in range(1, 10):
count[i] += count[i - 1]

# Place the elements in sorted order
i = size - 1
while i >= 0:
index = array[i] // place
output[count[index % 10] - 1] = array[i]
count[index % 10] -= 1
i -= 1

for i in range(0, size):
array[i] = output[i]

# Main function to implement radix sort
# Get maximum element
max_element = max(array)

# Apply counting sort to sort elements based on place value.
place = 1
while max_element // place > 0:
countingSort(array, place)
place *= 10

data = [121, 432, 564, 23, 1, 45, 788]
print(data)```

Java

```// Radix Sort in Java Programming

import java.util.Arrays;

// Using counting sort to sort the elements in the basis of significant places
void countingSort(int array[], int size, int place) {
int[] output = new int[size + 1];
int max = array;
for (int i = 1; i < size; i++) {
if (array[i] > max)
max = array[i];
}
int[] count = new int[max + 1];

for (int i = 0; i < max; ++i)
count[i] = 0;

// Calculate count of elements
for (int i = 0; i < size; i++)
count[(array[i] / place) % 10]++;

// Calculate cummulative count
for (int i = 1; i < 10; i++)
count[i] += count[i - 1];

// Place the elements in sorted order
for (int i = size - 1; i >= 0; i--) {
output[count[(array[i] / place) % 10] - 1] = array[i];
count[(array[i] / place) % 10]--;
}

for (int i = 0; i < size; i++)
array[i] = output[i];
}

// Function to get the largest element from an array
int getMax(int array[], int n) {
int max = array;
for (int i = 1; i < n; i++)
if (array[i] > max)
max = array[i];
return max;
}

// Main function to implement radix sort
void radixSort(int array[], int size) {
// Get maximum element
int max = getMax(array, size);

// Apply counting sort to sort elements based on place value.
for (int place = 1; max / place > 0; place *= 10)
countingSort(array, size, place);
}

// Driver code
public static void main(String args[]) {
int[] data = { 121, 432, 564, 23, 1, 45, 788 };
int size = data.length;
System.out.println("Sorted Array in Ascending Order: ");
System.out.println(Arrays.toString(data));
}
}
```

C

```// Radix Sort in C Programming

#include <stdio.h>

// Function to get the largest element from an array
int getMax(int array[], int n) {
int max = array;
for (int i = 1; i < n; i++)
if (array[i] > max)
max = array[i];
return max;
}

// Using counting sort to sort the elements in the basis of significant places
void countingSort(int array[], int size, int place) {
int output[size + 1];
int max = (array / place) % 10;

for (int i = 1; i < size; i++) {
if (((array[i] / place) % 10) > max)
max = array[i];
}
int count[max + 1];

for (int i = 0; i < max; ++i)
count[i] = 0;

// Calculate count of elements
for (int i = 0; i < size; i++)
count[(array[i] / place) % 10]++;

// Calculate cummulative count
for (int i = 1; i < 10; i++)
count[i] += count[i - 1];

// Place the elements in sorted order
for (int i = size - 1; i >= 0; i--) {
output[count[(array[i] / place) % 10] - 1] = array[i];
count[(array[i] / place) % 10]--;
}

for (int i = 0; i < size; i++)
array[i] = output[i];
}

// Main function to implement radix sort
void radixsort(int array[], int size) {
// Get maximum element
int max = getMax(array, size);

// Apply counting sort to sort elements based on place value.
for (int place = 1; max / place > 0; place *= 10)
countingSort(array, size, place);
}

// Print an array
void printArray(int array[], int size) {
for (int i = 0; i < size; ++i) {
printf("%d  ", array[i]);
}
printf("\n");
}

// Driver code
int main() {
int array[] = {121, 432, 564, 23, 1, 45, 788};
int n = sizeof(array) / sizeof(array);
printArray(array, n);
}```

C++

```// Radix Sort in C++ Programming

#include <iostream>
using namespace std;

// Function to get the largest element from an array
int getMax(int array[], int n) {
int max = array;
for (int i = 1; i < n; i++)
if (array[i] > max)
max = array[i];
return max;
}

// Using counting sort to sort the elements in the basis of significant places
void countingSort(int array[], int size, int place) {
const int max = 10;
int output[size];
int count[max];

for (int i = 0; i < max; ++i)
count[i] = 0;

// Calculate count of elements
for (int i = 0; i < size; i++)
count[(array[i] / place) % 10]++;

// Calculate cummulative count
for (int i = 1; i < max; i++)
count[i] += count[i - 1];

// Place the elements in sorted order
for (int i = size - 1; i >= 0; i--) {
output[count[(array[i] / place) % 10] - 1] = array[i];
count[(array[i] / place) % 10]--;
}

for (int i = 0; i < size; i++)
array[i] = output[i];
}

// Main function to implement radix sort
void radixsort(int array[], int size) {
// Get maximum element
int max = getMax(array, size);

// Apply counting sort to sort elements based on place value.
for (int place = 1; max / place > 0; place *= 10)
countingSort(array, size, place);
}

// Print an array
void printArray(int array[], int size) {
int i;
for (i = 0; i < size; i++)
cout << array[i] << " ";
cout << endl;
}

// Driver code
int main() {
int array[] = {121, 432, 564, 23, 1, 45, 788};
int n = sizeof(array) / sizeof(array);
printArray(array, n);
}```

## Complexity

Since radixsort is a non-comparative algorithm, it has benefits over comparative sorting algorithms.

For the radixsort that uses counting sort as an intermediate stable sort, the time complexity is O(d(n+k)).

Here, d is the number cycle and O(n+k) is the time complexity of counting sort.

Hence, radixsort has linear time complexity which is better than to O(nlog n) of comparative sorting algorithms.

In the event that we take extremely enormous digit numbers or the number of different bases like 32-bit and 64-bit numbers then it can act in linear time anyway the intermediate sort takes huge space.

This makes radix sort space inefficient. This is the reason why this sort isn’t used in software libraries.